# Fluid dynamics

Fluid mechanics isn’t taught at A level, so here are some of the concepts you’ll learn at university.

Buoyancy

Fluids exert an upwards force equal to the weight of the displaced fluid. This is called Archimedes’ principle. This can be shown on a free body diagram:

Fluid flow

Fluid flow can be represented by flow lines, which should the path of a particle in the flow:

Stream lines are curves whose tangent gives the velocity. When the flow lines and the stream lines are the same the flow is steady.

The mass of water entering a pipe must be equal to the mass leaving. This gives us:

This is called the continuity equation.

Bernoulli’s equation

We can use conservation of energy to derive Bernoulli’s equation:

This can be used to find velocity, height etc, but breaks down when there is viscosity.

Pascal’s law

This can be derived using a small layer of non compressible fluid:

At equilibrium the sum of the forces is zero:

This result is Pascal’s law.

Pressure applied is transmitted to every part of the fluid, so pressure, p, is the same at all points of the same height.

This means that heavy objects can be raised using hydraulic lift as force varies with area:

Gauge pressure = absolute pressure – atmospheric pressure

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